(41) Bulk Cylindrical Tank

[Albert Chan]

(10-15-2018 12:33 PM)Dieter Wrote:  Take a look at this sketch which should be quite exactly to scale:



Red solid line: elliptical dome top
Blue dotted line: spherical dome top

Very nice sketch. Thanks !

To get the 1943 gallon dome, I assumed the author was not stupid.
There must be a reason he measured R of 78" (not calculated 90")

If what he was doing is do get a fit with same cross section area, it all make sense.
With R=90", blue dotted line always under-estimated true dome volume.

With R=78", blue-dotted line will go pass the Dome Top.
This over-estimated area should cancelled out the lower under-estimated part.

Also, 6" liquid volume is better approximated as cylinder of 6" high. (Red line almost vertical)

For Elliptical Dome Top, I assumed bottom part of dome is a cyclinder, top part as elliptical dome.
Matching both tank height and tank volume. The revised dimensions is

Height = (slant height = 12) + (cylinder height = 190.67) + (elliptical dome height = 25.33)

With this revised numbers, the tank should match better to actual shape ...

Quote:Now imagine a radius of 75,22". That's not much more than the tank radius r, so the dome top section would be much higher than v₀ = 36" ...

That R were for a different dome shape, Spherical Segment Dome Top.
The dome is actually flat at v0 = 36", with radius = sqrt(2320) ~ 48.17"

You can confirm with this (set a1=72, a2=48.17, h=36): https://rechneronline.de/pi/spherical-segment.php